Scissor congruence

It is shown that certain simple figures can not be cut by scissors into pieces that can be reassembled to form certain other simple figures. The authors’ work was partially supported by National Science Foundation Grant G-14648 for Dubins, and Grant G-11594 for Hirsch.     

Bounds for certain integrals

A certain class of definite integrals is considered in which the integrand consists of a one-signed function together with another function which has a one-signed derivative in a certain interval. By examining the Cauchy form of the remainder, sets of bounds are developed which have a certain optimum property. The integrals may be multi-dimensional. The case in which the derivative component is not one-signed is briefly considered.     

Quasi-likelihood estimation for semimartingales

A technique of parameter estimation for a semimartingale based on the maximization of a likelihood type function is proposed. This technique is shown to be optimal in the sense of Godambe within a certain class of estimating equations. The resulting estimators are shown to be consistent and asymptotically normally distributed on certain events under relatively weak assumptions.     

Two optimality test for differentiable concave value functions in linear multi-objective programming problems

This note outlinestwo test which can be applied, under certain conditions, to solutions to linear multi-objective programming problems. The first test can be used to determine whether a given basic solution to the problem is optimal. The second test can be used to determine whether a given non-basic solution to the problem is optimal in a certain face of the set of feasible solutions of the problem.     

Some oscillatory properties of second order non linear differential equations

Summary The aim of this note is to show that, under certain conditions, the comparìson theorems between a nonlinear second order differential equation of certain type and a linear second order differential equation hold. From this we shall be able to guarentee the oscillatory or nonoscillatory character of certain or all solutions of the considered nonlinear differential equation. Work done at the Instituto Matematico ? Ulisse Dini ? in Firenze.     

Delone Sets with Finite Local Complexity: Linear Repetitivity Versus Positivity of Weights

We consider Delone sets with finite local complexity. We characterize the validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this context, we show that linear repetitivity is equivalent to positivity of weights combined with a certain balancedness of the shape of return patterns.     

Factorizations of certain q-series identities of Ramanujan and others

B. Yuttanan has shown that certain identities of Ramanujan and of Horie and Kanou can be factorized, that is, obtained by multiplying together certain pairs of identities. We give alternative, simpler factorizations of the same identities, and more.     

Locally polynomially bounded structures

We prove a theorem which provides a method for constructingpoints on varieties defined by certain smooth functions. Werequire that the functions be definable in a definably completeexpansion of a real closed field and be locally definable ina fixed o-minimal and polynomially bounded reduct. As an applicationwe show that in certain o-minimal structures, definable functionsare piecewise implicitly defined over the basic functions inthe language.     

On the titchmarsh convolution theorem for distributions on the circle

We prove a version of the Titchmarsh convolution theorem for distributions on the circle. We show that a certain “naïve” form of the Titchmarsh theorem can be violated, but only for the convolution of distributions with certain symmetry properties.     

Embedding relations in the lattice of recursively enumerable sets

Let ?* be the lattice of recursively enumerable sets of natural numbers modulo finite differences. We characterize the relations which can be embedded in ?* by using certain collections of maximal sets as domain and using Lachlan's notion of major subsets to code in the relation in certain natural ways. We show that attempts to prove the undecidability of ?* by using such embeddings fail.     

F分布密度曲线之变化

该文较深入地分析了特殊函数的某些性质,利用这些性质分析了F分布中不同参数所对应的密度曲线之间的位置关系.此外还讨论了密度曲线的某些渐近性质并建立了一些有关的方程.作为结论的应用及验证,作者给出了一些有代表性的例子.该文的分析方法还可用来讨论其它一些分布的密度曲线的某些性质.     

Interconnections of Markov chains and quasi-reversible queuing networks

A quasi-reversible queue can be associated with certain type of transactions of a Markov chain. It is shown that if Markov chains are coupled in a certain way, then to the resulting chain be associated a queuing network which is itself quasi-reversible and the stationary distribution of the chain takes the product form. The product form for mixed networks is derived from the result for open networks.     

Approximate Operators and Dual Extremum Principles for Linear Problems

The use of approximate operators in the theory of dual extremumprinciples is investigated for certain linear problems. If second-ordertrial functions to certain approximate Lagrangian equationscan be found, bounds which are improvements on the dual boundingfunctions can be constructed. Some simple applications to apartial differential equation and an integral equation are given.It is shown that both upper and lower bounds follow from onetrial function.     

具有常红利边界和延迟索赔的一类离散更新风险模型

考虑了具有常红利边界和延迟索赔的一类离散更新风险模型,其中间隔索赔到达时间从离散phase-type分布.定义了两种类型的索赔:主索赔和副索赔,主索赔以一定的概率引起副索赔且副索赔会以一定的概率被延迟到下一时段.通过引入辅助风险模型,推导了破产前红利折现期望满足的差分方程及其解.最后给出了当索赔额服从几何分布时的有关数值例子.     

H-SEPARABLE RINGS AND THEIR HOPF-GALOIS EXTENSIONS

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On the embeddability of certain infinitely divisible probability measures on Lie groups

We describe certain sufficient conditions for an infinitely divisible probability measure on a Lie group to be embeddable in a continuous one-parameter semigroup of probability measures. A major class of Lie groups involved in the analysis consists of central extensions of almost algebraic groups by compactly generated abelian groups without vector part. This enables us in particular to conclude the embeddability of all infinitely divisible probability measures on certain connected Lie groups, including the so called Walnut group. The embeddability is concluded also under certain other conditions. Our methods are based on a detailed study of actions of certain nilpotent groups on special spaces of probability measures and on Fourier analysis along the fibering of the extension.     

A reduction theorem for the linear complementarity problem with a certain patterned matrix

Matrices with a certain pattern are defined and their properties are studied. A reduction theorem is stated and proved which can be used to reduce the size of the linear complementarity problem defined by a matrix with the pattern. The identification of the pattern and the reduction theorem provide a mathematical model for a problem in structural mechanics when a certain symmetry prevails in the structural problem to be analyzed.     

Nonlinear singular perturbation problems: Proofs of correctness of a formal approximation based on a contraction principle in a Banach space

For many singular perturbation problems formal approximations of the solution can be constructed. Here it will be shown that correctness of a formal approximation of sufficiently high order can be proven if (i) certain a priori estimates for the solution of the linearized problem can be obtained and (ii) the remainder term of linearization satisfies a certain smallness condition. The proof will be based on a contractive mapping in a Banach space. Applications are given for singularly perturbed nonlinear second-order elliptic problems with boundary conditions of Dirichlet type.     

Superconvergence of collocation methods for a class of weakly singular Volterra integral equations

We discuss the application of spline collocation methods to a certain class of weakly singular Volterra integral equations. It will be shown that, by a special choice of the collocation parameters, superconvergence properties can be obtained if the exact solution satisfies certain conditions. This is in contrast with the theory of collocation methods for Abel type equations. Several numerical examples are given which illustrate the theoretical results.     

基于功能不完全可加系统的系统优化

为了揭示系统的某一功能达到最优与其所有子系统为实现系统这一功能而提供的功能之间的联系,探讨了功能不完全可加系统的系统优化过程,认为可通过对系统施加调节控制作用,使系统状态成功转移到期望状态的总成本最小来实现对系统的优化.最后辅以实例.